multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example
The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
 O. V. Widlund: Some recent applications of asymptotic error expansions to finite difference schemes
. Proc. Royal Soc. London, A 323, N. 1553 (1971), 167-177. MR 0495006
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